Limit - Research Article from Macmillan Science Library: Mathematics

Number Sequences

One way to examine limits is through a sequence of numbers. The following example shows a sequence of numbers in which the limit is 0.

The second number in the sequence, ½, is the result of dividing the first number in the sequence, 1, by 2. The third number in the sequence, ¼, is the result of dividing the second number in the sequence, ½, by 2.

This process of dividing each number by 2 to acquire the next number in the sequence is continued in order to acquire each of the remaining values. The three dots indicate that the sequence does not end with the last number that appears in the list, but rather that the sequence continues infinitely.

If the sequence continues infinitely, the values in the sequence will get closer and closer to 0. The numbers in the sequence, however, will never actually take on the value...